Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\dfrac{8}{3}$ $a_i = -\dfrac{3}{2}a_{i-1}$ What is $a_{2}$, the second term in the sequence?
From the given formula, we can see that the first term of the sequence is $-\dfrac{8}{3}$ and the common ratio is $-\dfrac{3}{2}$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = -\dfrac{8}{3} \cdot -\dfrac{3}{2} = 4$.